Does Disposition Drive Momentum?

Tyler Shumway and Guojun Wu∗

University of Michigan

March 15, 2005

Abstract

We test the hypothesis that the dispositon effect is a behavioral bias that drives stock pricemomentum. Using data from a large Shanghai brokerage firm, we estimate the magnitude ofthe disposition effect for a sample of 13,460 Chinese investors and firms. We find that a largemajority of Chinese investors exhibit the disposition effect. An investor’s disposition coefficientestimated with one year of data forecasts that investor’s disposition effect and investment per-formance in subsequent years. More disposition-prone investors tend to trade less frequentlyand in smaller sizes than other investors. While past returns do not forecast future returnsin our relatively short sample of Shanghai Stock Exchange stocks, sorting stocks by the netunrealized gains or losses of disposition-prone investors generates a statistically significant win-ner/loser spread of seven percent per year. Our results suggest that disposition does indeeddrive momentum.

∗Department of Finance, University of Michigan Business School, 701 Tappan Street, Ann Arbor, MI 48109.Shumway is visiting Stanford GSB for 2004-05, and can be reached at 650-725-9265 or shumway@umich.edu. Wucan be reached at 734-936-3248 or gjwu@umich.edu. We thank Charles Lee, Stefan Nagel, and seminar participantsat Barclay’s Global Investors for comments.

Introduction

Several researchers document that investors tend to hold assets on which they have experienced

paper losses, but they tend to sell assets on which they have experienced gains. Shefrin and Statman

(1985) call this the disposition effect, and they explain it with a combination of mental accounting

and risk-seeking in losses. Grinblatt and Han (2005) develop a model in which investors with the

disposition effect cause momentum in stock prices. We test the hypothesis that the disposition

effect is a behavioral bias, or that it is costly to those that exhibit it most strongly. We also test

the hypothesis that the disposition effect causes stock price momentum.

The disposition effect has been documented in stock markets by several authors, including Odean

(1998) and Grinblatt and Keloharju (2001). These and similar papers make a very convincing case

that investors exhibit disposition on average, but it is difficult to show that mental accounting or

some other behavioral bias causes disposition. One reasonable alternative explanation holds that

investors buy stocks based on private information. After buying, rising stock prices lead investors

to conclude that their information has been reflected in prices, but declining prices lead them to

conclude that their perceived mispricing has increased. We test the hypothesis that the dispostion

effect is a costly behavioral bias by examining the performance and characteristics of the investors

that exhibit the most disposition.

Momentum in stock prices is documented by Jegadeesh and Titman (1993) and a number

of subsequent authors. Grinblatt and Han (2005) present a relatively simple theory in which

momentum is driven by the disposition effect. Intuitively, if disposition-prone investors are holding

a stock for which good news is revealed, they will sell their shares as prices rise (as the disposition

effect predicts), decreasing any upward pressure on the stock price. Similarly, if disposition-prone

investors are holding a stock for which bad news is revealed, they will hold their shares rather

than sell on the news, again decreasing any downward pressure on the stock price. If any rational

investors trading against the disposition-prone investors do not fully adjust their demands for stocks

to account for the disposition bias, prices will take a relatively long time to converge to equilibrium

levels following large shocks. One implication of this theory is that the level of unrealized gains

or losses among disposition-prone investors is a sufficient statistic for future returns. Past returns

1

might predict future returns because they are a noisy proxy for unrealized gains or losses. Given

the transaction-level data that we have, we can test this hypothesis directly.

We examine our hypotheses with a large dataset of market transactions on the Shanghai Stock

Exchange. Using a hazard model, we estimate the magnitude of the disposition effect for each active

investor in our dataset. We believe that we are the first researchers to estimate the prevalence of

a behavioral bias at the investor level. Using our investor-level estimates of the disposition effect,

we test whether investors show consistent levels of dispostion over time and whether investors

that display strong disposition have weaker investment performance than other investors. We also

examine several other trading characteristics of investors that display strong disposition, looking

for evidence about their relative sophistication. We calculate the unrealized losses or gains for

disposition-prone investors in our data, and we regress future returns on past returns and our

unrealized gains variables.

We find that a large majority of Chinese investors exhibit the disposition effect. An investor’s

disposition coefficient estimated with one year of data forecasts that investor’s disposition effect

in subsequent years. Accounts that correspond to firms or brokerages show less disposition than

individual accounts. Individuals with more disposition in one year tend to have worse investment

performance in subsequent years. More disposition-prone investors tend to trade less frequently

and in smaller sizes than other investors. Surprisingly, more disposition-prone investors tend to

hold more diversified portfolios. We interpret our evidence as consistent with the hypothesis that

disposition is a costly behavioral bias.

Turning to momentum results, past returns do not forecast future returns in our relatively

short sample of Shanghai Stock Exchange stocks. However, sorting stocks by the net unrealized

gains or losses of all investors in our dataset generates a statistically and economically significant

“momentum-like” effect. Sorting stocks by the unrealized gains of particularly disposition-prone

investors generates a winner/loser spread of seven percent per year. We think this evidence is

consistent with the hypothesis that disposition drives momentum.

The next section discusses in more detail the hypotheses that we test and our methods for

testing them. The following section describes our data and compares it with other individual

investor datasets. Section III presents the results of our statistical tests, and section IV concludes.

2

I. Hypotheses and Methods

We want to test the hypotheses that the disposition effect is a costly behavioral bias and that it

drives momentum. This section describes and motivates our hypotheses in more detail. It also

describes the methods of our statistical tests.

A. Measuring Disposition

The most direct ways to examine the potential cost and effect of disposition require estimating the

extent to which individuals in our data exhibit the effect. Previous researchers have measured the

dispositon effect in a number of ways. Odean (1998) compares the proportion of losses realized to the

proportion of gains realized by a large sample of investors at a discount brokerage firm. Grinblatt

and Keloharju (2001) model the decision to sell or hold each stock in an investor’s portfolio by

estimating a logit model that includes each position on each day that an account sells any security

as an observation. Days in which an account does not trade are dropped from their analysis. A

potential problem with these and similar approaches is that they may give incorrect inferences in

cases in which capital gains or losses vary over time. Consider, for example, a security purchase

that results in an immediate capital gain, which is reversed only after a relatively long period of

time. If the investor holding this position sells the security immediately after the gain becomes

a loss, it will appear that the investor wanted to avoid realizing a loss even though the opposite

might be more correct.

We estimate the disposition effect with a Cox proportional hazard model with time-varying

covariates. Our time-varying covariates include daily observations on some market-wide variables

(5-day moving averages of return, return squared, and RMB volume) and daily observations on

whether each position corresponds to a capital loss or gain. One advantage of our method is that

the hazard model, which directly models the stock holding period, implicitly considers the selling

versus holding decision each day. Another advantage is that we can easily estimate our model for

each account with sufficient trades in our dataset.

Hazard models have been extensively applied in labor economics and other economic fields.

Proportional hazard models make the assumption that the hazard rate, λ(t), or the probability of

3

liquidation at time t conditional on being held until time t is,

λ(t) = φ(t)[exp(x(t)′β)], (1)

where φ(t) is referred to as the “baseline” hazard rate and the term exp(x(t)′β) allows the expected

holding time to vary across accounts and positions according to their covariates, x(t). The baseline

hazard rate is common to all the trades of one investor. Note that in this model the covariates may

vary with time. As mentioned above, each of our covariates changes daily. The Cox proportional

hazard model does not impose any structure on the baseline hazard, φ(t). Cox’s partial likelihood

estimator provides a way of estimating β without requiring estimates of φ(t). It can also handle

censoring of observations, which is one of the features of the data. Details about estimating the

proportional hazard model can be found in many places, including in Cox and Oakes (1984).

It is natural to ask whether either portfolio rebalancing or tax-loss selling will influence the

results of our disposition effect estimation. With respect to portfolio rebalancing, our investors

appear to hold tremendously undiversified portfolios, making rebalancing an unlikely concern. We

will give more evidence about the average level of diversification later in the text. With respect

to tax-loss selling, there is no capital gains tax in China. In fact, the only significant tax that

the investors in our data have to pay is a transactions tax that is equal to twenty basis points per

trade. Thus, it is quite unlikely that either taxes or rebalancing are significant motives for trade in

our data. The structure and tax environment of the Shanghai market is described in more detail

in Seasholes and Wu (2005).

B. Testing for Bias

The best existing evidence about the nature of the disposition effect is Odean (1998). Odean shows

that on average, individual investors at a large U.S. discount brokerage firm exhibit the disposition

effect. He also shows that on average, the trades that these investors place appear irrational. The

stocks that individual investors buy tend to underperform the stocks that they sell. Using a very

similar dataset, Coval, Hirshleifer and Shumway (2005) show that while on average the performance

of individual investors may be poor, some individual investors consistently outperform the market

4

on a risk-adjusted basis. Thus, it is possible that the investors that most strongly display the

disposition effect are informed investors. We exploit our ability to estimate the disposition effect

at the account level to examine this possibility.

One necessary condition for disposition to be a behavioral bias is that disposition is a stable,

predictable attribute of a particular investor. In the theory of Grinblatt and Han (2005), there

are both disposition-prone investors and rational investors that trade against each other. To be

consistent with their story, there should be substantial heterogeneity in the disposition displayed

by different investors and any given investor’s disposition effect should be more or less constant

over time. We examine these features of disposition by testing Hypothesis 1,

Hypothesis 1 There is persistent cross-sectional variation in the degree of the disposition effect

among individual investors.

We test this hypothesis by estimating the disposition effect at the investor level in two adjacent

time periods. Each set of estimates comes from a completely disjoint dataset. Any trades that are

not closed at the end of the first period are considered censored in the model estimated with first

period data. Therefore, any trades that are not closed at the end of the first period are completely

neglected in the model estimated with second period data. We test Hypothesis 1 by estimating

the rank correlation of account-level disposition coefficients over the two periods, and by testing

whether the rank correlation is signifcantly different from zero.

Clearly, if informed investors are successful at capturing the value of their information, their

investment performance will, on average, be better than that of relatively uninformed investors.

Thus, if the disposition effect is a manifestation of information trading, those that are particularly

disposition-prone should have higher overall stock returns than other investors. If, alternatively,

disposition is a behavioral bias, particularly disposition-prone investors should have lower overall

stock returns than other investors. We test this conjecture with Hypothesis 2,

Hypothesis 2 Investors with high disposition effect coefficients should have relatively poor invest-

ment performance.

We test this hypothesis by sorting investors into disposition quintiles based on their coefficients

estimated in one period and then examining stock returns by disposition quintile in subsequent

5

periods. To adjust for risk, we truncate long holding periods and estimate average betas and

standard deviations of holding period returns by quintile. We also regress holding period returns

on a number of control variables and disposition quintile.

While informed investors should have superior investment performance, they should also have

other characteristics that we associate with more sophisticated investors. This conjecture motivates

our third hypothesis,

Hypothesis 3 Investors with high disposition effect coefficients should appear less financially so-

phisticated than other investors.

We expect informed investors to have more total wealth than uninformed investors. While we do

not observe the wealth of our investors directly, we can observe some quantities that should be

correlated with wealth. We examine the average trade size and trade frequency of investors with

different disposition quintiles. We also examine the average diversification of different types of

investors. Finally, we estimate disposition coefficients for both individuals and corporate accounts.

If professionals are more sophisticated than individuals, corporate accounts should display less

disposition than individuals.

C. Disposition and Momentum

The most significant testable implication of the theory developed in Grinblatt and Han (2005) is

that the unrealized gains or losses of disposition-prone investors should be a sufficient statistic for

future returns. Conditional on unrealized gains or losses, past returns should have no predictive

power for future returns. Grinblatt and Han (2005) test this implication by constructing a proxy

for unrealized gains or losses. Their proxy basically compares the current price of a particular

stock to a volume-weighted past price. Their proxy for unrealized gains appears to drive out any

momentum variables in returns forecasting regressions. Frazzini (2005) constructs an unrealized

gain variable for mutual funds using data from Spectrum. While Frazzini (2005) cannot measure

unrealized gains precisely (Spectrum data are updated at most quarterly), he does find that his

unrealized gain variable has significant predictive power for future returns. Given the detailed

nature of the data that we have, we can test the implication of Grinblatt and Han (2005) in a more

direct way than previous studies.

6

Before looking at the relation between disposition and momentum, we examine the nature of

momentum in our Chinese data. Since past returns should be correlated with unrealized gains or

losses, we test Hypothesis 4,

Hypothesis 4 Returns should exhibit momentum - past winners should continue to outperform

while past loser underperform.

The Grinblatt and Han (2005) story holds that past returns are a proxy for unrealized gains, so

we expect past returns to be weak predictors of future returns. However, given our relatively short

sample, it seems likely that we will not have enough statistical power to estimate the momentum

relation very precisely.

Given the nature of our account-level transactions data, the most natural way to test the

hypothesis of Grinblatt and Han (2005) is to calculate unrealized gains or losses and use them to

predict future returns. We directly test Hypothesis 5,

Hypothesis 5 The unrealized gain or loss of all investors in our dataset should be a good predictor

of returns.

We construct our measures of unrealized losses or gains by comparing purchase prices to closing

prices. We adjust our returns calculations for stock splits and dividends. Once we have calculated

the total loss or gain on each open position in the dataset, we take shares-weighted averages of

unrealized gains for each stock. Finally, we sort stocks by their average unrealized gain or loss,

keeping the top decile of stocks as “winners” and the bottom decile as “losers.” We examine the

returns to a strategy that is long winners and short losers.

Finally, the Grinblatt and Han (2005) story stipulates that particularly disposition-prone in-

vestors drive momentum. Thus, we measure the unrealized gains or losses of more disposition-prone

and less disposition-prone investors separately. Using these two variables, we test our final hypoth-

esis,

Hypothesis 6 The unrealized gain of particularly disposition-prone investors should be a better

predictor of returns than the unrealized gain of less disposition-prone investors.

We regress future returns on the winner/loser strategy variable that corresponds to the unrealized

gains of more dispostion-prone and less disposition-prone investors.

7

Having access to account-level data allows us to examine the nature and impact of the disposition

effect in novel ways. To the best of our knowledge, researchers have not examined disposition at the

investor level before. We believe that we are the first researchers to examine whether disposition is a

persistent individual characteristic and to check whether cross-sectional heterogeneity in disposition

predicts subsequent performance. We are fairly confident that we are the first researchers to examine

the Grinblatt and Han (2005) hypothesis with more and less disposition-prone investors.

II. Data

We acquire a transaction-level dataset from a large brokerage firm in the city of Shanghai. We collect

all transactions (purchases or sales) that originate from our brokerage firm from the beginning of

2001 to March 12, 2004. A single trading record includes the following variables: transaction

date, transaction time, stock ticker, transaction price, size of trade in shares, time the buy order

was placed, time the sell order was placed, the trading account number of the buyer, and the

trading account number of the seller, the buyer’s brokerage office, and the seller’s brokerage office.

Account numbers allow us to identify and separate buyers and sellers into three groups: individuals,

corporations, and brokers. Some summary statistics for our account-level data appear in Panel A

of Table 1, and the number of trades and accounts in our data are described in the text below

Table 1.

Our dataset contains almost 17 million trades placed by 3.8 million different accounts. We are

confident that we have a complete trading record only for those accounts that correspond to our

Shanghai brokerage firm. The clients of our brokerage traded through 273,945 different accounts

and participated in 8.6 million transactions. There are a large number of relatively inactive accounts

at our brokerage firm. Of the more than 273 thousand accounts in our data, only 152 thousand

placed at least one trade in 2001. For much of our analysis, we require accounts to be fairly active

traders. In order to estimate the hazard model for holding period for a particular account, we

require the account to have at least seven closed trades (purchase and corresponding sale) within

the hazard model estimation period. Of the 152 thousand accounts that placed at least one trade

in 2001, 13,460 accounts have at least seven closed trades in 2001. The 13,460 accounts represent

8

our basic sample for much of the analysis in the paper.

The exchange mechanism adopted by the Shanghai Stock Exchange is an anonymous electronic

limit order market. Since our data contain both sides of each transaction, we can estimate the total

size of our brokerage firm by calculating the frequency with which clients from our firm are matched

in the trading process with other clients of our brokerage firm. Our firm’s clients are matched with

other clients of the same firm 2.09 percent of the time, so we conclude that the trades we examine

comprise approximately two percent of the transactions of the Shanghai Stock Exchange.

The average holding period of our investors is 28.5 trading days, but the median holding period

is just 8 trading days. We define the holding period as the time between an investor’s first purchase

of a security and the same investor’s first sale of the same security. The average returns of Shanghai

Stock Exchange stocks during our sample period is negative, and the average holding period return

of our investors is also negative. On average, our investors lose 1.43 percent of the value of their

trades over whatever period they hold the stocks in their portfolio. However, the median holding

period return is positive at 1.07 percent. Most of the trades that are opened during our sample

period are also closed during the period. Only 5.8 percent of all the positions in our dataset are

still open at the end of the sample. Translating the average trade size figures into dollar amounts

at the official exchange rate of RMB 8.28 = $1.00, the average trade value is $2624 and the median

trade size is $1085.

We also collect daily price data for all stocks traded on the Shanghai Stock Exchange. Our data

include a date variable, stock ticker, the stock’s opening price, closing price, maximum price, mini-

mum price, trading volume in shares, trading value in RMB, number of tradable shares outstanding

(free float), and total number of shares outstanding. We also collect corresponding information for

the major market composite index. Some summary statistics for our price data appear in Panel B

of Table 1.

Consistent with the negative average holding period returns in Panel A of Table 1, the average

quarterly return of Shanghai stocks is -3.41 percent, with a corresponding standard deviation of

16.65 percent. Most Shanghai stocks have prices between 4 and 30 RMB, with an average price of

11.5 RMB. Daily trading volumes are expressed in thousands of RMB, and seem consistent with the

average trade values reported above. The median stock, for example, experiences approximately

9

625 thousand dollars of volume per day.

Comparing our data to other individual investor datasets that are now available to researchers,

our data appear to have a few distinct advantages for examining whether disposition drives mo-

mentum. Comparing our data to the data available for a large discount brokerage firm in the U.S.

(e.g. Odean, 1998), we note that our dataset almost certainly represents a much larger fraction

of total market transactions than the discount brokerage firm data. Comparing our data to the

data available for investors in Finland (e.g. Grinblatt and Keloharju, 2001), we note that our data

include a much broader cross-section of stocks than that available in Finland. Grinblatt and Kelo-

harju use a sample of 88 Finnish stocks to test their hypotheses, while we have approximately 700

stocks for each of our momentum regressions. The biggest limitation of our sample is our relatively

short sample length. For the purpose of estimating momentum effects, we have only ten quarters

of data to analyze.

III. Results

Our results consist of hazard model estimates, average characteristics and performance of investors

by disposition quintile, and momentum results. We discuss each set of results in turn.

A. Hazard Model Estimates

The results of our hazard model estimations appear in Table 2. We estimate the hazard model for

all accounts with at least seven closed trades in 2001 and then we estimate it for all accounts with

at least seven closed trades in 2002. The data in Panel A of Table 2 report on coefficient estimates

from both years. While the dummy variable that indicates whether unrealized returns are positive

or negative appears to be statistically important in the hazard model, the other coefficients do not

appear to be important.

Given the structure of our model, a positive coefficient for the indicator variable I(Rit > 0)

indicates that an investor has the disposition effect. A coefficient of zero would imply that the

unrealized return has no effect on the investor’s hazard rate for closing the trade. The median

value of this coefficient, βd, is 1.66. This means that, holding all else equal, the median investor’s

10

conditional probability of selling a stock in his portfolio is exp(1.66) = 5.3 times higher for stocks

with gains than for stocks with losses. The average disposition coefficient for investors in our data

is 5.91 and a T-statistic testing the hypothesis that this average is zero is 22.71. More than ninety

percent of the estimated coefficients on the dummy variable are positive. Clearly, the data indicate

that the disposition effect is extremely strong among the Chinese investors in our sample.

Looking at the rank correlations in Panel B, it is clear that investors that display the disposition

effect in 2001 also tend to display the effect in 2002. The rank correlation of an investor’s coefficients

in both years is almost 45 percent, which is extremely statistically and economically significant.

The rank correlations of the other hazard model coefficients are all statistically significant but they

are economically fairly small. Based on the evidence of Table 1, we can conclude that our evidence

is quite consistent with Hypothesis 1. Most Chinese investors display the disposition effect, but

there appears to be substantial heterogeneity in the magnitude of the effect across individuals. An

investor’s level of disposition appears to be a stable investor characteristic.

B. Characteristics and Performance

Interestingly, the disposition effect for corporate and brokerage accounts reported in Table 2 is

significantly smaller than that for individuals. While we only have 62 observations on corporate

and brokerage accounts, the average βd for these accounts is only 2.05, and the median is just

1.02. Approximately 84 percent of corporate and brokerage accounts have positive values for βd.

This is a startling large quantity, but it is less than the more than ninety percent that holds for

individuals. These results suggest that investors with more disposition tend to be less sophisticated

than investors with less dispositon. Tables 3 and 4 explore this conjecture in much more detail.

Table 3 examines the investment performance of investors by disposition quintile. Panel A lists a

number of summary statistics by disposition quintile, including the average holding period return,

the number of days a position is held, the standard deviation of holding period return and the

average beta of the stocks that investors hold. Given the strength of the disposition effect among

these traders, converting holding period returns into equivalent daily or annual returns makes

little sense. Disposition coefficients are calculated using only data from 2001, and investment

performance is calculated using only data from 2002 onward. Market betas and other stock and

11

investor characteristics are also calculated using only data from 2001. The time over which holding

periods are calculated is either the actual investor’s holding period or twenty trading days, whichever

is shorter. The column labeled [% Days > 20] lists by disposition quintile the percentage of holding

period returns that are calculated by marking positions to market after 20 trading days.

The average holding period return of more disposition-prone investors is substantially lower

than that of less disposition-prone investors. In fact, average returns are monotonically decreasing

in disposition quintiles. Interestingly, average holding periods are monotonically increasing in

disposition quintiles. However, neither the standard deviation of returns nor the average market

beta of the stocks held seem to vary much by quintile. Average market betas are less than one

because our market index is a value-weighted index but the averages reported are equal-weighted

averages of individual stock betas. The buy-day return and sell-day return are listed to explore

whether investors with different levels of disposition behave differently with respect to liquidity.

There is a small amount of evidence that more disposition-prone investors are more willing to pay

the bid-ask spread upon closing a position, but differences in trading styles does not appear to be

driving the relative underperformance of more dispositon-prone investors.

Panel B of Table 3 reports on the statistical significance of disposition in explaining holding

period returns in a regression context. Each holding period return is an observation in the regres-

sions, and the regressions contain disposition quintile, a number of stock characteristics, and finally

two other account characteristics. When dispostion quintile is included in this regression as the

lone explanatory variable, its coefficient is economically and statistically significant. Going from

the lowest disposition quintile to the highest quintile reduces the expected holding period return

by −0.088 ∗ 4 = −0.352, or by thirty-five basis points. In Model 2, including the market beta of

the stock has no effect on the coefficient for disposition quintile. In Model 3, including the stocks

average squared return, its average daily trading value and its average high price minus low price

squared actually makes the coefficient on disposition quintile more negative. In Model 4, includ-

ing the average 2001 performance of the investor and the investor’s average 2001 holding period

makes disposition quintile insignificant. These variables are apparently highly correlated with the

investor’s disposition coefficient. Our evidence appears to be consistent with Hypothesis 2. The

investment performance of particularly disposition-prone investors appears to be somewhat worse

12

than that of other investors.

Table 4 describes some other characteristics of investors by disposition quintile. Less disposition-

prone investors trade in larger sizes and more frequently than more dispositon-prone investors.

Trade size and frequency are proxies for investor wealth in our sample. We cannot observe in-

vestor wealth, but since margin trades and short sales are restricted in China, wealthier investors

can be identified by the magnitude of their trades. More dispositon-prone investors tend to hold

more stocks in their portfolios, with average holdings of 3.2 stocks versus 1.6 stocks for the least

disposition-prone. Given that the most disposition-prone investors have the longest holding peri-

ods, the worst performance, and the most diversification, it appears that these investors are only

holding onto losers, which make them diversified even though they continue to have abnormally

negative returns. This is consistent with the findings of Kumar (2004), who finds that stocks held

by less diversified investors have higher average returns than other stocks. Given that corporate and

brokerage accounts display less disposition and that less disposition-prone investors are probably

wealthier than their more dispostion-prone peers, our evidence is largely consistent with Hypothesis

3. Investors with a particularly strong dispositon effect appear to be less financially sophisticated

than other investors.

Overall, it appears that more disposition-prone investors are less financially sophisticated and

have worse performance than other investors. This implies that it is relatively unlikely that these

investors are informed investors trading in a disposition-like manner to maximize their expected

utility. It seems much more likely that the disposition effect is a costly behavioral bias. We explore

whether disposition imposes costs on other investors by affecting prices in the next section.

C. Momentum

All of our regressions related to momentum are reported in Table 5. We construct several momentum-

related variables by sorting stocks by the variable of interest (either past returns or unrealized gains)

into deciles at the end of each quarter. We then label stocks in the top decile as “winners” and

stocks in the bottom decile as “losers.” Finally, we construct a variable that is equal to one for

winners, minus one for losers, and zero for all other stocks. After defining this variable for each

quarter, we regress the returns of all stocks in each quarter on the value of our winner/loser vari-

13

able at the end of the previous quarter and a series of dummy variables for each quarter in the

data. When calculating quarterly stock returns, we drop all stocks that have not traded in previous

quarters to avoid unusual returns in the first weeks of IPO stock trading.

In constructing our momentum variable, we sort stocks on returns calculated from the beginning

of each quarter until five trading days before the end of the quarter. We drop the last five trading

days of returns in order to avoid any bid-ask bounce or extremely short-term price momentum or

reversal effects. In constructing our average unrealized gain variables, we take the unrealized gain

to be the return on the stock from an investor’s purchase date until five days before the end of the

relevant quarter. We drop stocks that are sold in the five days before the relevant end of quarter

date from our calculations. Having unrealized gains at the transaction level, we calculate average

unrealized gains at the stock level by multiplying the unrealized gain or loss of each investor in our

data by the number of shares the investor purchased. Next, we average this quantity across our

investors, and finally we divide the resulting average unrealized RMB loss by the total free float

of the stock. This yields something like the shares-weighted average unrealized gain or loss of our

investors.

Looking at Table 5, we examine the momentum effect at the Shanghai Stock Exchange in Model

1. During this ten quarter period, the momentum effect in Shanghai goes in the wrong direction.

The coefficient on our winner/loser momentum variable is negative, but it is neither statistically

nor particularly economically significant. We are not able to reject Hypothesis 4. There is no

apparent momentum in Shanghai data during the period of our study.

Model 2 regresses our first average unrealized gain variable on future returns. The unrealized

gain variable in Model 2 is calculated with all of the holdings of all of the investors in our dataset

that trade through our brokerage. Thus, for example, this variable is calculated by taking the

average unrealized gain or loss over about 276 thousand positions at the end of December of 2002.

Our unrealized gain variable has a very statistically and economically significant coefficient of 1.37,

with an associated T-statistic of 4.491. Our regression coefficient can be interpretted as the average

return of an equal-weighted portfolio of winners minus the average return of an equal-weighted1It should be noted that our T-statistic is calculated with one large regression that contains all stock returns over

all quarters, with a total sample size of 6834. If we estimate our regression with a Fama-Macbeth procedure, thecoefficient is almost the same but the corresponding T-statistic drops to 1.05.

14

portfolio of losers. Average excess returns of 1.37 percent per quarter translate into an expected

annual excess return of 5.59 percent.

Model 3 combines our unrealized gain measure with past returns in one regression. The unre-

alized gain coefficient becomes larger and more significant while the past returns variable becomes

more negative and statistically significant. Apparently, in this particular sample, returns measured

over the past quarter are not a particularly good proxy for unrealized gain or losse. Considering

the results of Models 2 and 3, our results are consistent with Hypothesis 5. The average unrealized

gain or loss of investors is an excellent predictor of future returns. This momentum-like variable

even predicts returns over a time period in which momentum itself fails to predict returns.

According to the Grinblatt and Han (2005) model, the returns of particularly disposition-prone

investors should be a better predictor of future returns than either past returns or the unrealized

gains of all investors. Models 4 through 7 examine this particular prediction by constructing the

unrealized gain or loss variable for various subsets of our investor population. In Model 4, we

examine the predictive ability of the unrealized gain variable calculated only with the positions

of those investors in our dataset that have a positive disposition coefficient. This unrealized gain

variable predicts returns quite well, with a coefficient of 1.183 and a T-statistic of 3.88. Next, we

calculate the unrealized gains variable for investors with βd above and below the median value of βd.

We regress returns on the associated winner/loser variables in Models 5 through 7. These variables

are calculated with much less data than the unrealized gain variable for all investors described

above. For example, while the unrealized gain variable on December 31, 2002 for all investors that

trade through our brokerage is based on 276 thousand positions, the unrealized gain variable for

investors with above the median disposition is calculated at the same time with only about 31

thousand positions.

Despite being calculated with many fewer positions, Models 5 through 7 show that the unreal-

ized gain variable of particularly disposition-prone investors is the best predictor of future returns

we can construct. The unrealized gain coefficient in Model 5 is the most economically and sta-

tistically significant coefficient in Table 5. The implied portfolio excess return that corresponds

with quarterly returns of 1.709 percent is 7.01 percent per year. Including both the winner/loser

variable corresponding to above median βd investors and that which corresponds to below median

15

βd investors makes the latter variable insignificant. This is strong evidence in favor of our sixth

hypothesis. It is the unrealized gains of particularly disposition-prone investors that predicts future

returns, not past returns or the unrealized gains of all investors.

IV. Conclusion

We test whether the disposition effect is a costly behavioral bias and whether it might cause

stock price momentum. Our account-level data allow us to perform some powerful tests of the

hypotheses that we pose. Our evidence is consistent with the assertion that the disposition effect

is a behavioral bias. Investors that exhibit the bias most strongly in one period have inferior

investment performance in subsequent periods. They also trade less frequently and in smaller sizes.

Accounts associated with corporations or brokerage firms exhibit significantly less disposition than

individuals. While past returns do not predict future returns in this sample, the average unrealized

gain or loss of our investors is a good predictor of future returns. Constructing unrealized gain

variables with the trades of particularly disposition-prone investors yields the best predictor of

future returns that we can generate. Disposition appears costly to investors, and it does appear to

drive momentum.

16

References

Coval, Joshua D., David Hirshleifer, and Tyler Shumway, 2005, Can individual investors beat themarket? working paper, University of Michigan.

Coval, Joshua D. and Tyler Shumway, 2005, Do behavioral biases affect prices? Journal of Finance60, 1-34.

Cox, David R. and D. Oakes, 1984, Analysis of Survival Data, Chapman and Hall, New York.

Frazzini, Andrea, 2005, The disposition effect and under-reaction to news, working paper, YaleUniversity.

Grinblatt, Mark and Bing Han, 2005, Prospect theory, mental accounting, and momentum,forthcoming, Journal of Financial Economics.

Grinblatt, Mark and Matti Keloharju, 2001, What makes investors trade? Journal of Finance56, 589-616.

Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers:Implications for market efficiency, Journal of Finance 48, 65-91.

Kumar, Alok, 2004, Diversification decisions of individual investors and asset prices, working paper,University of Notre Dame.

Odean, Terrance, 1998, Are investors reulctant to realize their losses? Journal of Finance 53,1775-1798.

Seasholes, Mark S., and Guojun Wu, 2005, Predictable behavior, profits, and attention, workingpaper, University of Michigan.

Shefrin, Hersh and Meir Statman, 1985, The disposition to sell winners too early and ride loserstoo long: Theory and evidence, Journal of Finance 40, 777-91.

17

Table 1: Summary Statistics

Table 1 provides summary statistics on the sample used throughout the paper. Panel A describesthe trades in the account-level data, while Panel B describes the stock-level data. The account-levelsample runs from January 2, 2001 through March 12, 2004, while the stock-level data runs overa slightly longer time period. The account-level sample consists of all accounts which completeat least seven trades in 2001 (both purchase and sale). The stock-level data consists of all stockstraded on the Shanghai Stock Exchange. In the account-level data, there are 1,133,194 trades and13,460 accounts, or about 26 trades per account per year on average. In the stock-level data, thereare 817 stocks traded over 819 days, resulting in a total sample size of 557,848.

Panel A: Account-Level DataVariable Mean Std Dev Median 1 Percent 99 PercentHolding Period (days) 28.5 60.4 8.0 0.0 321.0Return -1.429 10.223 1.067 -37.451 17.965I(Trade Left Open) 0.058 0.235 0.000 0.000 1.000Trade Size 21732 117683 8988 1063 190270

Panel B: Stock-Level DataVariable Mean Std Dev Median 1 Percent 99 PercentQuarterly Return -3.41 16.65 -5.56 -33.93 45.08Daily Price 11.53 5.52 10.39 3.88 29.83Daily RMB Volume (000) 12946 37319 5176 0 122499

Sample Quantities of Interest:

Total accounts = 3,826,549Accounts from our brokerage (OB) = 273,945OB accounts with at least 1 trade in 2001 = 152,010OB accounts with at least 7 round-trip trades in 2001 = 13,460

Total trades = 16,930,868Total OB trades = 8,642,632Total trades of OB traders with ≥ 1 trade in 2001 = 6,955,910Total trades of OB traders with 7 trades in 2001 = 1,133,194

Our brokerage represents about 2.09 percent of all trading in Shanghai stocks

18

Table 2: Estimates of the Disposition Effect

Table 2 reports summary statistics for the coefficient estimates of the Cox proportional hazardmodel,

λ(t) = φ(t)[exp(β0 + βdI(ri,t > 0) + βvVm,t + βsσm,t + βr r̄m,t)],

where t is the time to position liquidation, λ(t) is the hazard rate for liquidation, φ(t) is referredto as the “baseline” hazard rate and the exponential term allows the hazard rate to vary acrosstrades according to whether the investor has a positive or negative return on the stock, I(ri,t > 0),the average market volume (in Yuan) over the past five trading days, Vm,t, the average marketreturn squared over the past five trading days, σm,t, and the average market return over the pastfive days, r̄m,t. A positive estimate for βd is consistent with the disposition effect. The baselinehazard rate, φ(t), is common to all the trades of one individual. The table reports statistics forindividual accounts and corporate accounts separately. The model is estimated for each accountthat closes at least seven trades in 2001 and for each account that closes at least seven trades in2002. Panel A reports summary statistics on all estimated coefficients while Panel B reports therank correlations of each account’s coefficient estimates using only data from 2001 and the samecoefficients using only data from 2002.

Panel A: Coefficient EstimatesIndividual Investor Accounts in 2001 and 2002 - 23794 Obs

Mean Std Dev T-Stat Median % Positive 1 Percent 99 Percentβd 5.91 40.12 22.71 1.66 90.30 -1.82 55.87βv -0.44 130.31 -0.52 -0.08 46.92 -18.32 20.35βs 0.09 7.40 1.96 0.01 61.35 -0.68 1.09βr 1.31 134.61 1.51 0.08 54.00 -9.85 21.82

Corporate and Brokerage Accounts in 2001 and 2002 - 62 ObsMean Std Dev T-Stat Median % Positive 1 Percent 99 Percent

βd 2.05 4.41 3.66 1.02 83.87 -0.71 24.14βv -0.10 3.19 -0.23 0.04 53.22 -16.23 7.02βs 0.01 0.10 0.64 0.01 59.68 -0.23 0.59βr 0.37 1.08 2.67 0.09 59.68 -1.33 4.23

Panel B: Rank Correlations, 2001 Versus 2002Individuals Only - 5653 Obs

Spearman Corr P-Valueβd 44.58 0.0000βv 6.20 0.0000βs 4.48 0.0008βr 8.59 0.0000

19

Table 3: Predicting Performance with Disposition

Table 3 examines the cross-sectional relation between disposition and performance. All of thestatistics reported in Table 3 use disposition coefficients and other statistics estimated with 2001transactions data to predict investment performance from 2002 through the end of the sample.Panel A gives means by disposition quintile. βd is the disposition effect coefficient from the hazardmodel described in Table 2. The average return listed in Column 3 is calculated over either theinvestor’s holding period or the first 20 days of the investors holding period, whichever is shorter.The buy return in Column 4 is the return from the purchase price to the day’s closing price, and thesell return is similarly the return from the selling price to the day’s closing price. Days Held lists theaverage holding period for completed transactions, Days > 20 lists the percentage of holding periodsgreater than 20 days, and the last two columns of Panel A list the standard deviation and marketbeta, respectively, of the average holding of each quintile’s investor. Panel B gives the resultsof several returns regressions. All of the quantities that returns are regressed on are calculatedwith data from 2001. Returns are regressed against the investor’s disposition quintile, the stock’smarket beta, the stock’s average daily high price minus its low price squared, the logarithm of thestock’s average daily trade value, the stocks average squared return, the investor’s average holdingperiod return, and the investor’s average holding period in days, both from 2001. T-statistics arein parentheses.

Panel A: Means by Disposition Quintile - 328255 ObsQuint βd Return Buy Ret Sell Ret Days Held % Days > 20 σ(HPRet) βi,m

1 -0.05 -0.26 0.07 0.00 31.88 17.88 6.10 0.612 0.98 -0.28 0.10 -0.04 36.97 21.21 6.10 0.603 1.74 -0.34 0.11 -0.04 48.79 27.18 6.28 0.604 2.75 -0.53 0.07 -0.03 63.37 34.29 6.55 0.605 17.83 -0.61 0.07 -0.03 85.22 41.85 6.89 0.60

Panel B: Returns Regressions - 279558 ObsVariable Model 1 Model 2 Model 3 Model 4Intercept -0.236 -0.172 -6.30 -0.114

(-11.60) (-5.47) (-10.73) (-1.74)βd Rank -0.088 -0.088 -0.092 -0.012

(-9.48) (-9.50) (-9.95) (-1.22)βi,m -1.060 0.003 0.005

(-2.66) (0.08) (0.13)Mean (PHi

i,t − PLoi,t )2 -0.343 -0.358

(-9.76) (-10.19)ln(Vi) 0.017 0.190

(10.66) (11.05)Mean r2

i,t -0.922 -0.939(-6.49) (-6.62)

Acct. Mean Ret 0.237(3.53)

Acct. Mean Days -0.053(-15.58)

20

Table 4: Disposition and Investor Characteristics

Table 4 describes the cross-section of accounts in a little more detail. The table lists average accountcharacteristics for the 13460 accounts with at least seven trades in 2001. Each characteristic iscalculated with post-2001 data. The second column gives the average number of stocks held byeach account on each of the 10 quarter-ends from the end of 2001 through the end of the firstquarter of 2004. The third column lists the average trade size of each type of account, in Yuan.The fourth column lists the average number of trades placed by each account from the end of 2001to the end of the sample.

Quint Stocks Held Trade Value Trades1 1.611 31333 45.182 2.232 24115 50.253 2.914 19764 46.754 3.333 17792 37.995 3.205 15889 23.81

21

Table 5: Disposition and Momentum

Table 5 describes the results of seven momentum-style regressions. Each regression forecasts thereturns of momentum portfolios measured over three months. Each independent variable is equalto one, zero, or minus one, for each stock in each quarter. The variable called “Momentum,” forexample, is set to one for stocks in the highest decile of returns in the previous quarter, it is setto minus one for stocks in the lowest decile of returns in the previous quarter, and it is set tozero for all other stocks. Similarly, the unrealized gains or losses variables (UR Gains) are set toone for stocks that rank in the top decile of unrealized gains, minus one for stocks in the bottomdecile, which generally have unrealized losses, and zero for all other stocks. The unrealized gainor loss variable is calculated with the positions of all investors in our dataset (All), the positionsof all disposition-effect investors (βd > 0), the positions of investors with greater than the mediandisposition (βd > Med), and the positions of investors with less than the median disposition (βd <Med). The sample size is 6834 for each regression, corresponding to approximately 683 stocks perquarter over the 10 quarters for which we have data. Each regression also contains (unreported)dummy variables to control for each quarter. T-statistics are reported in parentheses.

Dependent Variable: Quarterly Returns from 2002:1 to 2004:2Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Momentum -0.550 -0.919

(-1.79) (-2.91)UR Gain (All) 1.370 1.582

(4.49) (5.05)UR Gain (βd > 0) 1.183

(3.88)UR Gain (βd > Med) 1.709 1.494

(5.57) (4.29)UR Gain (βd < Med) 1.160 0.457

(3.78) (1.31)

22